Subgroups — C₃×C₅×#498 #11751473

Order 960.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₃×C₅×#106	C₂	1	4	yes	maximal
3	C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#498	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×Q₈	—	2	2	no	—
6	C₂×C₃×C₅×C₈	C₂²	1	2	yes	—
7	C₃×C₅×C₄⋊C₄	—	2	2	no	—
8	C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
9	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₃×#498	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₄⋊Q₈	C₂×C₃	1	2	yes	—
12	C₅×#106	C₂×C₃	1	4	yes	—
13	C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic
14	C₃×C₅×Q₈	—	4	4	no	—
15	C₂×C₃×C₄×C₅	—	2	4	no	—
16	C₂×C₃×C₄×C₅	D₄	1	2	yes	—
17	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₃×C₅×C₈	Q₈	1	4	yes	complemented
19	C₃×C₄⋊Q₈	C₂×C₅	1	2	yes	—
20	C₃×#106	C₂×C₅	1	4	yes	—
21	C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic
22	C₂×C₅×Q₈	—	2	2	no	—
23	C₂×C₅×C₈	C₂²×C₃	1	2	yes	—
24	C₅×C₄⋊C₄	—	2	2	no	—
25	C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
26	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
27	#498	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²×C₃×C₅	C₂×D₄	1	1	yes	characteristic
29	C₃×C₄×C₅	—	4	4	no	—
30	C₃×C₄×C₅	SD₁₆	1	4	yes	—
31	C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
32	C₂×C₃×Q₈	—	2	2	no	—
33	C₂×C₃×C₈	C₂²×C₅	1	2	yes	—
34	C₃×C₄⋊C₄	—	2	2	no	—
35	C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
36	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
37	C₅×Q₈	—	4	4	no	—
38	C₂×C₄×C₅	—	2	4	no	—
39	C₂×C₄×C₅	C₃×D₄	1	2	yes	—
40	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
41	C₅×C₈	C₃×Q₈	1	4	yes	complemented
42	C₄⋊Q₈	C₂×C₃×C₅	1	2	yes	—
43	#106	C₂×C₃×C₅	1	4	yes	—
44	C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic
45	C₂×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₃×C₅	C₂×SD₁₆	1	2	yes	—
47	C₃×Q₈	—	4	4	no	—
48	C₂×C₃×C₄	—	2	4	no	—
49	C₂×C₃×C₄	C₅×D₄	1	2	yes	—
50	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
51	C₃×C₈	C₅×Q₈	1	4	yes	complemented
52	C₂²×C₅	C₂×C₃×D₄	1	1	yes	characteristic
53	C₄×C₅	—	4	4	no	—
54	C₄×C₅	C₃×SD₁₆	1	4	yes	—
55	C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
56	C₂×Q₈	—	2	2	no	—
57	C₂×C₈	C₂²×C₃×C₅	1	2	yes	—
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
60	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
61	C₃×C₅	#498	1	1	yes	characteristic, direct product factor, Hall
62	C₂²×C₃	C₂×C₅×D₄	1	1	yes	characteristic
63	C₃×C₄	—	4	4	no	—
64	C₃×C₄	C₅×SD₁₆	1	4	yes	—
65	C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
66	C₂×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₅	C₂×C₃×SD₁₆	1	2	yes	—
68	Q₈	—	4	4	no	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	C₃×C₅×D₄	1	2	yes	—
71	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
72	C₈	C₃×C₅×Q₈	1	4	yes	complemented
73	C₂×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₃	C₂×C₅×SD₁₆	1	2	yes	—
75	C₅	C₃×#498	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	C₂×C₃×C₅×D₄	1	1	yes	characteristic
77	C₄	—	4	4	no	—
78	C₄	C₃×C₅×SD₁₆	1	4	yes	—
79	C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
80	C₃	C₅×#498	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
82	C₂	C₂×C₃×C₅×SD₁₆	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₅×#498	C₃	direct (N × H)
10. C₃×#498	C₅	direct (N × H)
18. C₃×C₅×C₈	Q₈	semidirect
27. #498	C₃×C₅	direct (N × H)
41. C₅×C₈	C₃×Q₈	semidirect
51. C₃×C₈	C₅×Q₈	semidirect
61. C₃×C₅	#498	direct (N × H)
72. C₈	C₃×C₅×Q₈	semidirect
75. C₅	C₃×#498	direct (N × H)
80. C₃	C₅×#498	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#106	2
C₃×C₄×C₅×C₈	2
C₅×#498	3
C₃×#498	5

Subgroups — C3×C5×#498 #11751473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#498 #11751473